Abel's Identity

Abel's Identity Unlocking the beauty😍 of Math — one concept at a time. | We create video solutions to Math problems

A nice way to find x...💯 x^x = 2⁶⁴
22/12/2025

A nice way to find x...💯 x^x = 2⁶⁴

Finding the inverse of a 3×3 matrix. 💯
21/12/2025

Finding the inverse of a 3×3 matrix. 💯

Enjoy this awesome solution 💯💡
20/12/2025

Enjoy this awesome solution 💯💡

🧠 Direct Proof vs Proof by ContradictionIn mathematics, the truth of a statement is established through proof, not intui...
19/12/2025

🧠 Direct Proof vs Proof by Contradiction

In mathematics, the truth of a statement is established through proof, not intuition.
Two of the most powerful proof methods are direct proof and proof by contradiction.

✔️ Direct Proof:

A direct proof starts from known facts, definitions, or axioms and proceeds step-by-step until the conclusion is reached.

Example:
Claim: If a number is even, then its square is even.

Proof:
Let n = 2k for some integer k.
Then:
n² = (2k)² = 4k² = 2(2k²),

Therefore, the claim is true.

This proof shows the conclusion explicitly.

❌ Proof by Contradiction:

A proof by contradiction assumes the opposite of what you want to prove, then shows that this assumption leads to an impossibility.

Example:
Claim: √2 is irrational.

Proof:
Assume √2 is rational.
Then it can be written as a/b in lowest terms.
This leads to both 'a' and 'b' being even — a contradiction.

Thus, the assumption is false, and the claim is true.

🔍 Key Difference

• Direct proof builds the truth step by step.

• Contradiction proves truth by eliminating all alternatives.

Both are logically sound and equally valid.

📐 When to Use Each:

• Use direct proof when the conclusion follows naturally from definitions.

• Use contradiction when direct paths are blocked or unclear.

Mathematics chooses clarity — not preference.

💡A proof does not convince by persuasion.
It convinces by necessity.

Once the logic is correct, the conclusion cannot be denied.

A beautiful way to tackle this type of logarithmic problem. 💯
19/12/2025

A beautiful way to tackle this type of logarithmic problem. 💯

A beautiful solution to a beautiful problem. Enjoy 😊
18/12/2025

A beautiful solution to a beautiful problem. Enjoy 😊

🔢 Syllogisms, Deduction, and Mathematics.Mathematics is not built on opinions.It is built on deductive arguments.Every t...
17/12/2025

🔢 Syllogisms, Deduction, and Mathematics.

Mathematics is not built on opinions.
It is built on deductive arguments.

Every theorem, formula, and proof follows a logical structure where conclusions are forced by premises — not guessed, voted on, or assumed.

🧠 Syllogism in Mathematics:

A syllogism is a special kind of deductive argument with a fixed structure:

• Major premise
• Minor premise
• Conclusion

Example (Mathematical Syllogism):

• All numbers divisible by 4 are even.
• 28 is divisible by 4.
• Therefore, 28 is even.

This is how mathematics thinks.

⚖️ Validity vs Soundness (Mathematical Lens)

A mathematical argument is valid if the conclusion follows logically from the assumptions.

It is sound if:

1. The reasoning is valid, and
2. The assumptions (axioms, definitions, givens) are true.

That’s why in mathematics:

• Correct logic + false assumptions = false result
• Correct logic + true assumptions = guaranteed truth

❌ Valid but Unsound (Math Example)

• All prime numbers are even.
• 7 is a prime number.
• Therefore, 7 is even.

The structure is valid. The premise is false. The conclusion fails.

📐 This is why proofs begin with:

• “Given…”
• “Let…”
• “Assume…”

Mathematics demands:

• clear premises
• strict deduction
• unavoidable conclusions

No shortcuts.

💡In a world full of opinions,
mathematics teaches us that truth is proven — not asserted.

Deduction doesn’t persuade... It compels.

Shout out to my newest followers! Excited to have you onboard! እንከባበር እንዳንሰባበር, Shivam Sharma, Sk Bhai Sk Bhai, Joseph K...
17/12/2025

Shout out to my newest followers! Excited to have you onboard! እንከባበር እንዳንሰባበር, Shivam Sharma, Sk Bhai Sk Bhai, Joseph Kollie, Jul Tesh, Florence Emoefe, Obaidul Islam

A nice logarithmic equation coupled with a nice solution. 📌
16/12/2025

A nice logarithmic equation coupled with a nice solution. 📌

This is a nice problem on circle geometry. You should try it. 💪
15/12/2025

This is a nice problem on circle geometry. You should try it. 💪

What's wrong here?
15/12/2025

What's wrong here?

It’s been a while… but Abel’s Identity is back.Thank you for staying. More meaningful posts ahead. 🙏 No videos for now, ...
14/12/2025

It’s been a while… but Abel’s Identity is back.
Thank you for staying. More meaningful posts ahead. 🙏 No videos for now, as laptop needs fixing. But we keep moving. 💪

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